WASHINGTON — The Republican presidential candidates are rolling out a variety of tax-cutting plans that benefit the wealthiest Americans and will make the challenge of national debt even bigger.

Texas Gov. Rick Perry’s economic plan, for example, cuts the top rates for individual and corporate taxes. He would eliminate capital gains taxes and give taxpayers an option of paying under the current system or at the lower rate of a 20 percent flat tax. The current top rate for the wealthiest taxpayers is 35 percent.

Since taxpayers are likely to choose the less expensive alternative, analysts say, Perry’s plan would reduce rates without broadening the base of those paying income taxes — a near-certain recipe for lower government revenue.

Perry and GOP presidential candidates like Herman Cain and Newt Gingrich (who want to cut the top tax rate more than Perry) say they’ll capture the difference by prompting economic growth. The more income businesses and wealthy entrepreneurs are able to keep, the more they’ll invest in economic activities that create jobs, Perry and other Republican candidates argue.

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But since the onset of the recession, after-tax profits have soared while capital investments languish. The Federal Reserve’s Flow of Funds report from September shows after-tax corporate profits up $173.6 billion since 2007, while capital investments are running at a pace $27.6 billion below the level achieved in 2006.

Among the leading candidates, Mitt Romney has outlined the least radical changes in taxes. He starts with an expensive premise, however — making permanent the tax cuts enacted during President George W. Bush’s administration. Those tax cuts are scheduled to expire in December 2012. Extending them for the next 10 years would add more than $4 trillion to the deficit, according to the nonpartisan Congressional Budget Office.

Texas Rep. Ron Paul would abolish the income tax.

The leading candidates have all proposed eliminating estate taxes. Romney wants to eliminate capital gains taxes for those making less than $200,000 a year, while all the other candidates want to eliminate capital gains taxes for everyone.

The tax applies to sales of personal property such as real estate and stocks. The current rate for capital gains taxes is 15 percent.

If the Republican plans seem to favor the rich, conservatives say that’s only fair.

Pam Villarreal, a senior fellow at the National Center for Policy Analysis in Dallas, said the wealthiest Americans have seen their taxes rise more than most Americans.

“The tax burden of the top few earners has increased far more than the tax burden of the bottom 50 percent,” she said.

The wealthiest 20 percent of Americans paid more than two-thirds of income taxes in 2009, according to an analysis by the Washington-based Tax Policy Center.

Republicans in Congress have made cutting the federal budget deficit their top priority this year, while refusing Democratic attempts to raise taxes. Republican proposals to change the tax laws are usually described as “revenue-neutral” — bringing in the same amount as current tax laws by broadening the number who pay taxes, but with lower tax rates.

Jared Bernstein, a senior fellow at the Center on Budget and Policy Priorities, and chief economic adviser to Vice President Joe Biden until last spring, called the loss of revenue a “huge” problem with the Perry plan.

“Because the Perry plan allows you to either pay a flat tax rate of 20 percent or sign onto the current system, it’s got to be a big revenue loser. You can either pay what you owe now, or you pay less,” Bernstein said last week at an election preview session sponsored by National Journal.

Alex Brill, a former chief economist with the House Ways and Means Committee who is now at the conservative American Enterprise Institute, said that does not mean the presidential candidates are out of step with the Republican Party’s emphasis on balancing the federal budget.

“Republicans are trying to hold the line on spending and guard against a tax increase,” he said. “If the economy grows, and taxes don’t grow faster than the economy, and spending grows more slowly than the economy — if those things hold, we will get our deficits under control.”

Brill conceded that Perry’s plan would create a significant cut in tax revenue, but he noted that the candidates are selling their plans as tax simplification rather than the big tax cuts featured in former President George W. Bush’s 2000 campaign.

Former Utah Gov. Jon Huntsman’s plan for eliminating all deductions in favor of income tax rates of 8 percent, 14 percent and 23 percent, for example, is billed as a revenue-neutral proposal. Huntsman would reduce the corporate rate to 25 percent from the current 35 percent.

“If we were to make Bush tax cuts permanent, is that a tax cut?” Brill asked. “Yes, because these tax policies are scheduled to expire. To make them permanent is a loss of revenue relative to current law. On the other hand, it’s not a tax cut. It just keeps the same system in place for the future that we have today.”

Perry’s plan would eliminate taxation of Social Security benefits. But it is unclear on some points, such as continuation of the Bush-era tax cuts. An analysis by the Tax Policy Center, after getting no response from Perry’s campaign, concluded that his approach would let the cuts expire as scheduled at the end of 2012.

Even with that, however, the Center estimates Perry’s plan reduces federal revenue by at least $570 billion by 2015.

Cain’s plan is summed up in his “9-9-9” slogan — a flat tax of 9 percent on income, a 9 percent national sales tax and a corporate tax rate of 9 percent. That would reduce taxes for the wealthiest Americans and American companies but would raise taxes for 80 percent of the public, according to the Tax Policy Center.

The plan would be revenue-neutral in the sense that it would raise as much revenue as current tax law, the center found.

Cain has modified his plan to exempt from taxation those living below the poverty line.

The Republican candidates rely on getting economic growth back above 3 percent a year to meet their budget goals, and on a supply-side approach that expects lower tax rates will create more tax revenue because of growth.